Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q3 of degree 3

Introduction

Polynomial Invariants #Aut Splitting Field Number of
j Ramification Polygon Slopes Residual Polynomials fT eT #Gal Gal Polynomials Extensions
1{(1,1), (3,0)}[ 1/2 ](z+1){1}12{ 6 }{ 3T2 }132·32·3
(z+2){1}12{ 6 }{ 3T2 }13
2{(1,2), (3,0)}[ 1 ](z2+1){1}21{ 6 }{ 3T2 }132·32·3
(z2+2){3}11{ 3 }{ 3T1 }33
3{(1,3), (3,0)}[ 3/2 ](z+2){1}12{ 6 }{ 3T2 }3323232